There are a number of processes for producing foam-backed upholstery or cushion portions comprising a cover with a core of a foam material on the inside thereof. DE 36 27 221 A1 discloses such a process for producing a foam-backed upholstery or cushion portion wherein the cover of the cushion portion is clamped between two parts of a clamping frame, defining a hollow space or cavity therein, whereupon the clamping frame is positioned between two parts or halves of a mold. A reaction mixture is then introduced into the cavity formed within the cover, and the reaction mixture, on foaming up, urges the cover into contact against the inside surfaces of the two mold portions. A reduced pressure can be applied to the mold portions in known manner to ensure that the cover bears in a snug and wrinkle-free manner against the inside surfaces of the mold portions. It will be seen therefore that that process requires the reaction mixture to be introduced between the edges of the cover and thus between the two components making up the clamping frame which holds the cover in position. In terms of apparatus structure, that requires a not inconsiderable level of expenditure, while in addition the operation of introducing the reaction mixture into the cavity defined by the cover also involves a not inconsiderable amount of time.